A multiphase design strategy for dealing with participation bias

A recently funded study of the impact of oral contraceptive use on the risk of bone fracture employed the randomized recruitment scheme of Weinberg and Wacholder (1990, Biometrics 46, 963-975). One potential complication in the bone fracture study is the potential for differential response rates between cases and controls; participation rates in previous, related studies have been around 70%. Although data from randomized recruitment schemes may be analyzed within the two-phase study framework, ignoring potential differential participation may lead to biased estimates of association. To overcome this, we build on the two-phase framework and propose an extension by introducing an additional stage of data collection aimed specifically at addressing potential differential participation. Four estimators that correct for both sampling and participation bias are proposed; two are general purpose and two are for the special case where covariates underlying the participation mechanism are discrete. Because the fracture study is ongoing, we illustrate the methods using infant mortality data from North Carolina.